2017青岛赛区亚洲区域赛网络赛 1011题题解

忘是亡心i 2022-06-08 06:14 184阅读 0赞

Problem Description  
  
A cubic number is the result of using a whole number in a multiplication three times. For example, 3×3×3=27 so 27 is a cubic number. The first few cubic numbers are 1,8,27,64 and 125. Given an prime number p. Check that if p is a difference of two cubic numbers.  
  
  
  
  
Input  
  
The first of input contains an integer T (1≤T≤100) which is the total number of test cases.  
For each test case, a line contains a prime number p (2≤p≤1012).  
  
  
  
  
Output  
  
For each test case, output 'YES' if given p is a difference of two cubic numbers, or 'NO' if not.  
  
  
  
  
Sample Input  
  
10  
2  
3  
5  
7  
11  
13  
17  
19  
23  
29  
  
  
  
  
  
Sample Output  
  
NO  
NO  
NO  
YES  
NO  
NO  
NO  
YES  
NO  
NO

思路：若能找到一个整数n满足 p=3n²+3n+1 则为YES（好不容易找到的规律）

#include <iostream>
    #include <cstdio>
    #include <cstring>
    #include <queue>
    #include <cmath>
    #include <algorithm>
    #include <vector>
    #include <map>
    #include <string>
    #include <stack>
    #define LL long long
    #define INF 0x7fffffff
    #define MAX 200010
    #define PI 3.1415926535897932
    #define E 2.718281828459045
    using namespace std;
    int t;
    LL p;
    int main()
    {
        scanf("%d",&t);
        while(t--){
            scanf("%lld",&p);
            bool flag=false;
            p=p-1;
            if(p%3==0){
                p=p/3;
                LL n=(LL)sqrt(1.0*p);
                if(n*n+n==p) flag=true;
            }
            if(flag)printf("YES\n");
            else printf("NO\n");
        }
        return 0;
    }